1. Field of the Invention
The present invention relates to the petroleum industry and more particularly to the development of underground reservoirs such as petroleum reservoirs or gas storage sites which allows modification of a representation of the reservoir, referred to as “reservoir model”, in order to make the reservoir model coherent with the various data collected in the field.
2. Description of the Prior Art
Optimization and development of petroleum reservoirs are based on the most accurate possible description of the structure, the petrophysical properties, the fluid properties, etc., of the reservoir being studied. A software tool accounting for these aspects in an approximate way is a “reservoir model.” A reservoir model is a model of the subsoil, representative of both its structure and its behavior. Generally, this type of model which is represented in a computer is referred to as a “numerical model.” A reservoir model comprises generally a three-dimensional grid, associated with one or more petrophysical property maps (porosity, permeability, saturation, etc.). The association assigns values of these petrophysical properties to each cell of the grid.
These models which are well known and widely used in the petroleum industry, allow determination of many technical parameters relative to the study or the development of a reservoir, such as a hydrocarbon reservoir. In fact, since the reservoir model is representative of the structure of the reservoir and of the behavior thereof, engineers use it, for example, in order to determine which zones are the most likely to contain hydrocarbons, the zones in which it may be interesting/necessary to drill an injection or a production well in order to enhance hydrocarbon recovery, the type of tools to use, and the properties of the fluids to be used and recovered, etc. These interpretations of reservoir models in terms of “technical development parameters” are well known. Similarly, modelling CO2 storage sites allows monitoring these sites, to detect abnormal behaviors and to predict the displacement of the injected CO2.
The purpose of a reservoir model thus is to best account for all the available information on a reservoir. A reservoir model is representative when a reservoir simulation for this model provides historical data estimations that are very close to the observed data. What is referred to as historical data are the production data obtained from measurements in wells in response to the reservoir production (oil production, water production of one or more wells, gas/oil ratio (GOR), production water proportion (water cut)), and/or repetitive seismic data (4D seismic impedances in one or more regions, etc.). A reservoir simulation is a technique allowing simulation of fluid flows within a reservoir by means of software referred to as “flow simulator” and of the reservoir model.
Integration of all the available data is therefore essential. These data generally comprise:                measurements at certain points of the geological formation, in wells for example. These data are referred to as “static” because they are invariable in time (on the scale of the reservoir production times),        “historical data”, comprising production data, for example the fluid flow rates measured in wells, tracer concentrations and data obtained from repetitive seismic acquisition campaigns at successive times. These data are referred to as dynamic because they evolve during the development and they are indirectly linked with the properties assigned to the cells of the reservoir model.        
Techniques for integration of dynamic data (production and/or 4D seismic) in a reservoir model are known which are referred to as “history matching” techniques.
History matching modifies the parameters of a reservoir model, such as permeabilities, porosities or well skins (representing damages around the well), fault connections, etc., in order to minimize the differences between the simulated and measured historical data. The parameters can be linked with geographic regions, such as permeabilities or porosities around one or more wells. The difference between real data and simulated data forms a functional referred to as objective function. The history matching problem is solved by minimizing this functional.
The optimization loop is as follows. The petrophysical properties (lithofacies, porosities, permeabilities, etc.) are generated in a first grid and all of these data make up the geological model of the reservoir. Since the geological grid can be relatively fine, these properties are upscaled to a coarser grid, referred to as flow grid, in order to reduce the computation times during simulation. The production record is then simulated in this grid. This simulation allows computing well production data, as well as water, oil and gas saturation and pressure maps at different times. When 4D seismic data are available, these maps are transmitted to a petro-elastic model that computes the seismic attributes of the model. These seismic attributes and simulated production data are then compared with the data measured via the objective function.
The grid used by the petro-elastic model can have a finer resolution than the flow grid, or it can be identical to that of the geological model. A stage of downscaling the pressure and saturation maps of the flow grid to the seismic grid is then necessary. If the flow grid was constructed by agglomerating the cells of the petro-elastic model, a simple way of carrying out this downscaling assigns the pressures and the saturations of a cell of the flow grid to the underlying fine cells. This method is however not accurate in practice because it does not account for the underlying heterogeneities within a coarse cell. Now, the spatial variations of the pressure and the distribution of the saturations greatly depend on the absolute and relative permeabilities and porosities present on the fine scale. If these heterogeneities are not taken into account, computation of the seismic attributes becomes less accurate because the impedances are themselves sensitive to the pressure and saturation variations. Downscaling the pressures and the saturations thus aims to compute seismic attributes that are more representative of the geological model and to reduce the error introduced through upscaling.
There are known techniques allowing this pressure and saturation downscaling to be performed. A state of the art and a new technique are presented in the following document:                S. A. Castro, A Probabilistic Approach to Jointly Integrate 3D/4D Seismic, Production Data and Geological Information for Building Reservoir Models, PhD thesis, Stanford University, 2007.        
This document presents two techniques using only static data (absolute permeabilities, porosities, percentage of shale, etc.) for improving saturation downscaling and it also provides a solution based on local flow simulations. In the paragraphs below, each of these techniques is briefly presented.
A first solution recalculates a saturation distribution in each coarse cell using the porosities present on the fine scale, that is:S(u)=S(v)φ(u)/ φ(v)∀u⊂v 
In the above equation, u designates a fine cell included in a coarse cell v, S one of the three saturations, φ the porosity and φ(v) the arithmetic mean of the porosity in cell v.
In:                M. Sengupta, Integrating Rock Physics and Flow Simulation to Reduce Uncertainties in Seismic Reservoir Monitoring, PhD thesis, Stanford University, 2000,1D downscaling of the saturations is carried out along the wells using data provided by the logs (porosities, permeabilities, percentage of shale, etc.). This downscaling then allows calculation of more accurate amplitude variations in the wells.        
The two aforementioned algorithms are purely statistical and they do not use data such as pressures and saturations in the initial state, relative permeabilities, etc. Castro proposed another saturation downscaling algorithm based on local flow simulations. Reconstruction is achieved by iterating in the coarse cells while following the direction of flow and using the saturations calculated upstream as the boundary conditions.